A common technique in communication systems with unreliable and time-varying channel conditions is to correct errors based on automatic repeat request (ARQ) schemes together with a forward error correction (FEC) technique called hybrid ARQ (HARQ). If an error is detected by a commonly used cyclic redundancy check (CRC), the receiver of the communication system requests the transmitter to send additional information (data packets retransmission) to improve the probability of correctly decoding the erroneous packet.
A packet will be encoded with the FEC before transmission. Depending on the content of the retransmission and the way the bits are combined with previously transmitted information, S. Kallel, Analysis of a type II hybrid ARQ scheme with code combining, IEEE Transactions on Communications, Vol.38, No. 8, August 1990 and S. Kallel, R. Link, S. Bakhtiyari, Throughput performance of Memory ARQ schemes, IEEE Transactions on Vehicular Technology, Vol.48, No. 3, May 1999 define three different types of ARQ schemes:                Type I: The erroneous received packets are discarded and a new copy of the same packet is retransmitted and decoded separately. There is no combining of earlier and later received versions of that packet.        Type II: The erroneous received packets are not discarded, but are combined with additional retransmissions for subsequent decoding. Retransmitted packets sometimes have higher coding rates (coding gain) and are combined at the receiver with the stored soft-information from previous transmissions.        Type III: Is the same as Type II with the constraint each retransmitted packet is now self-decodable. This implies that the transmitted packet is decodable without the combination with previous packets. This is useful if some packets are damaged in such a way that almost no information is reusable. If all transmissions carry identified data, this can be seen as a special case called HARQ Type III with a single redundancy version.        
HARQ Type II and III schemes are obviously more intelligent and show a performance gain with respect to Type I, because they provide the ability to reuse information from of previously received erroneous packets. There exist basically three schemes of reusing the redundancy of previously transmitted packets:                Soft-Combining        Code-Combining        Combination of Soft- and Code-CombiningSoft-Combining        
Employing soft-combining the retransmission packets carry identical information compared with the previously received information. In this case the multiple received packets are combined either by a symbol-by-symbol or by a bit-by-bit basis as for example disclosed in D. Chase, Code combining: A maximum-likelihood decoding approach for combining an arbitrary number of noisy packets, IEEE Trans. Commun., Vol. COM-33, pp. 385–393, May 1985 or B. A. Harvey and S. Wicker, Packet Combining Systems based on the Viterbi Decoder, IEEE Transactions on Communications, Vol. 42, No. 2/3/4, April 1994.
In case of employing symbol-level combining, the retransmitted packets have to carry identical modulation symbols to the previously transmitted erroneous packets. In this case the multiple received packets are combined at modulation symbol level. A common technique is the maximum ratio combining (MRC), also called average diversity combining (ADC), of the multiple received symbols, where after N transmissions the sum/average of the matching symbols is buffered.
In case of employing bit-level combining the retransmitted packets have to carry identical bits to the previously transmitted erroneous packets. Here, the multiple received packets are combined at bit level after demodulation. The bits can be either mapped in the same way onto the modulation symbols as in previous transmissions of the same packet or can be mapped differently. In case the mapping is the same as in previous transmissions also symbol-level combining can be applied. A common combining technique is the addition of calculated log-likelihood ratios (LLRs), especially if using so-called Turbo Codes for the FEC as known for example from C. Berrou, A. Glavieux, and P. Thitimajshima, Near Shannon Limit Error-Correcting Coding and Decoding: Turbo-Codes, Proc. ICC '93, Geneva, Switzerland, pp. 1064–1070, May 1993; S. Le Goff, A. Glavieux, C. Berrou, Turbo-Codes and High Spectral Efficiency Modulation, IEEE SUPERCOMM/ICC '94, Vol. 2 , pp. 645–649, 1994; and A. Burr, Modulation and Coding for Wireless Communications, Pearson Education, Prentice Hall, ISBN 0-201-39857-5, 2001. Here, after N transmissions the sum of the LLRs of the matching bits is buffered.
Code-Combining
Code-combining concatenates the received packets, in order to generate a new code word (decreasing code rate with increasing number of transmission). Hence, the decoder has to be aware of how to combine the transmissions at each retransmission instant in order to perform a correct decoding (code rate depends on retransmissions). Code-combining offers a higher flexibility with respect to soft-combining, since the length of the retransmitted packets can be altered to adapt to channel conditions. However, this requires more signaling data to be transmitted with respect to soft-combining.
Combination of Soft- and Code-Combining
In case the retransmitted packets carry some symbols/bits identical to previously transmitted symbols/bits and some code-symbols/bits different from these ones, the identical code-symbols/bits are combined using soft-combing as described in the section titled “Soft-Combining” while the remaining code-symbols/bits will be combined using code-combining. Here, the signaling requirements will be similar to code-combining.
It has been shown in M. P. Schmitt, Hybrid ARQ Scheme employing TCM and Packet Combining, Electronics Letters Vol. 34, No. 18, September 1998 that HARQ performance for Trellis Coded Modulation (TCM) can be enhanced by rearranging the symbol constellation for the retransmissions. There, the performance gain results from the maximizing the Euclidean distances between the mapped symbols over the retransmissions, because the rearrangement has been performed on a symbol basis. Considering high-order modulation schemes (with modulation symbols carrying more than two bits) the combining methods employing soft-combining have a major drawback: The bit reliabilities within soft-combined symbols will be in a constant ratio over all retransmissions, i.e. bits which have been less reliable from previous received transmissions will still be less reliable after having received further transmissions and, analogous, bits which have been more reliable from previous received transmissions will still be more reliable after having received further transmissions. Generally, HARQ schemes do not take into account the variations in bit-reliabilities. These variations downgrade the decoder performance significantly. Mainly, the variations result from two reasons.
First, the varying bit reliabilities evolve from the constraint of two-dimensional signal constellation mapping, where modulation schemes carrying more than 2 bits per symbol cannot have the same mean reliabilities for all bits under the assumption that all symbols are transmitted equally likely. The term mean reliabilities is consequently meant as the reliability of a particular bit over all symbols of a signal constellation.
Employing a signal constellation for a 16 QAM modulation scheme according to FIG. 1 showing a Gray encoded signal constellation with a given bit-mapping order i1q1i2q2, the bits mapped onto the symbols differ significantly from each other in mean reliability in the first transmission of the packet. In more detail, bits i1 and q1 have a high mean reliability, as these bits are mapped to half spaces of the signal constellation diagram with the consequences that their reliability is independent from the fact of whether the bit transmits a one or a zero.
In contrast thereto, bits i2 and q2 have a low mean reliability, as their reliability depends on the fact of whether they transmit a one or a zero. For example, for bit i2, ones are mapped to outer columns, whereas zeros are mapped to inner columns. Similarly, for bit q2, ones are mapped to outer rows, whereas zeros are mapped to inner rows.
For the second and each further retransmissions the bit reliabilities will stay in a constant ratio to each other, which is defined by the signal constellation employed in the first transmission, i.e. bits i1 and q1 will always have a higher mean reliability than bits i2 and q2 after any number of retransmissions.
Second, employing partly soft-combining, suppose that all transmitted bits would have identical reliability after the first transmission. Even then variations in bit reliabilities would be introduced over retransmissions, because reliabilities for those bits which are retransmitted (and soft-combined) would increase, whereas reliabilities of not retransmitted bits would stay unchanged. Moreover, bits which are not transmitted in the first transmission and then transmitted in retransmissions (transmitting additional redundancy) emphasize this effect.
In co-pending PCT/EP01/01982 a method has been suggested that in order to enhance the decoder performance, it would be quite beneficial to have equal or near to equal mean bit reliabilities after each received transmission of a packet. Hence, the bit reliabilities are tailored over the retransmissions in a way that the mean bit reliabilities get averaged aged out. This is achieved by choosing a predetermined first and at least second signal constellation for the transmissions, such that the combined mean bit reliabilities for the respective bits of all transmissions are nearly equal. I.e. bits which have been highly reliable in the first transmission are mapped in such a way that they become less reliable in the second transmission and vice versa.
Hence, the signal constellation rearrangement results in a changed bit mapping, wherein the Euclidean distances between the modulation symbols can be altered from retransmission to retransmission due to the movement of the constellation points. As a result, the mean bit reliabilities can be manipulated in a desired manner and averaged out to increase the performance the FEC decoder at the receiver.